To find the area of the figure which consists of a rectangle combined with a right triangle, we can break it down into two parts: the area of the rectangle and the area of the triangle.
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Area of the Rectangle: The area \( A \) of a rectangle is calculated as: \[ A = \text{length} \times \text{width} \] In this case, we have:
- Length (top side) = 8 cm
- Width (left side) = 4 cm
Therefore, the area of the rectangle is: \[ A_{rectangle} = 8 , \text{cm} \times 4 , \text{cm} = 32 , \text{cm}^2 \]
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Dimensions and Area of the Triangle: The triangle is right-angled at the bottom left corner, with:
- Base (bottom side of the triangle) = 10 cm
- Height (left side of the triangle) = 4 cm
The area \( A \) of a triangle is calculated as: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \] Hence, the area of the triangle will be: \[ A_{triangle} = \frac{1}{2} \times 10 , \text{cm} \times 4 , \text{cm} = \frac{1}{2} \times 40 , \text{cm}^2 = 20 , \text{cm}^2 \]
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Total Area of the Figure: To get the total area of the figure, we add the area of the rectangle and the area of the triangle: \[ A_{total} = A_{rectangle} + A_{triangle} = 32 , \text{cm}^2 + 20 , \text{cm}^2 = 52 , \text{cm}^2 \]
Thus, the area of the figure is 52 square centimeters.